Millersville University/Department of Mathematics

A First Course in Partial Differential Equations

This page links to resources supporting the textbook, A First Course in Partial Differential Equations, written by Robert Buchanan and Zhoude Shao, and published by World Scientific and Imperial College Press.

• Textbook errata
• Students' solutions manual

The remaining links are to Java source code files for examples and exercises from the textbook chapter on finite difference techniques for approximating solutions to partial differential equations.

• Explicit method for approximating the solution to the heat equation with homogeneous Dirichlet boundary conditions. This method is used to generate the data plotted in Figs. 12.2-12.4.
• Crank-Nicolson implicit method for approximating the solution to the heat equation with homogeneous Dirichlet boundary conditions. This method is used in Example 12.1.
• Crank-Nicolson implicit method for approximating the solution to the heat equation with homogeneous Robin boundary conditions.
• Explicit method for approximating the solution to the wave equation with homogeneous Dirichlet boundary conditions. This method is used in Example 12.2.
• Implicit method for approximating the solution to the wave equation with homogeneous Dirichlet boundary conditions. This method is used in Example 12.3.
• Jacobi iterative method for appoximating the solution to a linear system of equations. This method is used in Example 12.6.
• Gauss-Seidel iterative method for appoximating the solution to a linear system of equations. This method is used in Example 12.7.
• Use of the Gauss-Seidel iterative method to approximate the solution to Laplace's equation. This method is used to generate the data plotted in Fig. 12.10.
• A comparison of the Gauss-Seidel and Successive Over-Relaxation methods for approximating the solutions to linear systems of equations. This program is used to generate the data tabulated in Example 12.8.
• Use of the Successive Over-Relaxation method to approximate the solution to Poisson's equation. This method is used in Example 12.9.
• Solution to Exercise 08.
• Solution to Exercise 09.
• Solution to Exercise 10.
• Solution to Exercise 11.
• Solution to Exercise 12.
• Solution to Exercise 13.
• Solution to Exercise 14.
• Solution to Exercise 17.
• Solution to Exercise 18.
• Solution to Exercise 20.